brainpopfandomcom-20200223-history
Factoring/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby Moby spreads grout on a bathroom wall. Tim holds up a blue tile. TIM: Hey Moby, I thought we agreed on white tiles for the bathroom. Moby beeps. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, what is factoring? From, Ramona. TIM: Well, factoring a number is like breaking it into pieces. A label appears, reading and factoring. TIM: Each of those pieces is called a factor. A label appears, reading: factor. TIM: As you might remember from our Multiplication movie, factors are the numbers we multiply together to get a product. An equation appears, reading, 5 times 3 equals 15. 5 and 3 are labeled, factors. 15 is labeled, product. TIM: Put another way, factoring is the process of finding all the numbers that a number is divisible by. Let’s look at all the different ways we can arrange 12 tiles on the wall. Here we’ve got one row of 12 tiles: 12 times 1 equals 12. On-screen, one row of 12 tiles appears. TIM: 6 times 2 also equals 12. On-screen, two rows of six tiles appear. TIM: And 3 times 4 will get you to 12, too! On-screen, three rows of four tiles appear. TIM: Our little tiling experiment shows that 12 is divisible by 1, 12, 2, 6, 3, and 4. That means these numbers are all factors of the number 12. A number appears, reading, 12. Its factors appear below it: 1, 12, 2, 6, 3, and 4. Moby beeps. TIM: What can we use factoring for? I’ll tell you. This wall is 250 centimeters by 350 centimeters. On-screen, a rectangular section of the wall appears. The sides are labeled, 250 centimeters and 350 centimeters. TIM: We can use factoring to figure out exactly what size tile we should use if we want all the tiles to fit perfectly! Moby beeps. TIM: Okay, what are all the numbers that 250 is divisible by? Moby beeps. The number, 250, appears. Its factors appear below it: 1, 250, 2, 125, 5, 50, 10, and 25. TIM: Good! Now what about 350? Moby beeps. The number, 350, appears. Its factors appear below it: 1, 350, 2, 175, 5, 70, 14, 25, 7, 50, 10, and 35. TIM: As you can see, some factors show up in the lists for both numbers. We call these common factors. A label appears, reading, common factors. Numbers that appear in both lists are highlighted: 1, 2, 5, 10, 25, and 50. TIM: Assuming our tiles are square, we can pick ones whose sides are equal to any of those common factors. 2 by 2, 5 by 5, 10 by 10, 25 by 25, and 50 by 50 tiles would all work. On-screen, progressively larger tiles fill up the wall. TIM: If I wanted to lay as few tiles as possible, I’d pick the biggest factor that both 250 and 350 have in common. Moby beeps. TIM: Right, 50! We give this number a special name: the greatest common factor, or GCF. A label appears, reading, greatest common factor, GCF. Moby beeps. He holds up a tile that's as big as his body. TIM: Um, yeah. That was just a hypothetical example. We won’t actually use tiles that big. Moby beeps. TIM: I’m glad you asked that question! You may have noticed that some of the factors we’ve found so far, like 2, 5, and 7, are prime numbers, which are whole numbers greater than 1, that are only divisible by 1 and themselves. A label appears, reading, prime numbers. TIM: Since these factors are prime numbers, we call them prime factors. A label appears, reading, prime factors. TIM: But what about the factors that aren’t prime? Moby beeps. TIM: That’s right, we can keep factoring them until we eventually end up with all prime numbers! The process of breaking any number into its smallest whole pieces is called prime factorization. A label appears, reading, prime factorization. TIM: To do it, we use something called a factor tree. A label appears, reading, factor tree. TIM: Um, I think I need something to write on. Moby uses his finger laser to cut a piece of the wall, about the size of a sheet of paper. He pulls the piece away from the wall and holds up a pencil. TIM: Whoa! Okay, let’s try 24. I usually factor 24 by thinking of it as 2 times 12. Moby writes the equation, 24 equals 2 times 12, on the piece of wall. TIM: 2 is prime, so we're done there, but 12 can be factored into 3 and 4. Moby writes, 3 times 4, below 12. TIM: Now we’ve got 2 and 3, which are prime factors, but 4 can still be factored. Moby writes, 2 times 2, below 4. TIM: So the prime factorization of 24 is 2 times 3 times 2 times 2. Moby holds up the piece of wall. The factors branch downward, resembling a tree. Moby beeps. TIM: Well, it works the same with negative numbers. Just remember that negative 1 will always be a factor of any negative number. Moby beeps. TIM: Yeah, once you understand what's going on, factoring is easier than tiling a bathroom! On-screen, Tim looks around at the mess they've made on the wall. TIM: A lot easier. Remind me not to let Mom and Dad come up here anytime soon. Category:BrainPOP Transcripts